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An h-adaptive RKDG method with troubled-cell indicator for two-dimensional hyperbolic conservation laws

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Abstract

In Zhu and Qiu (J Comput Phys 228:6957–6976, 2009), we systematically investigated adaptive Runge-Kutta discontinuous Galerkin (RKDG) methods for hyperbolic conservation laws with different indicators, with an objective of obtaining efficient and reliable indicators to obtain better performance for adaptive computation to save computational cost. In this follow-up paper, we extend the method to solve two-dimensional problems. Although the main idea of the method for two-dimensional case is similar to that for one-dimensional case, the extension of the implementation of the method to two-dimensional case is nontrivial because of the complexity of the adaptive mesh with hanging nodes. We lay our emphasis on the implementation details including adaptive procedure, solution projection, solution reconstruction and troubled-cell indicator. Extensive numerical experiments are presented to show the effectiveness of the method.

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Authors and Affiliations

  1. School of Natural Science, Nanjing University of Posts and Telecommunications, Nanjing, Jiangsu, 210046, People’s Republic of China

    Hongqiang Zhu

  2. School of Mathematical Sciences, Xiamen University, Xiamen, Fujian, 361005, People’s Republic of China

    Jianxian Qiu

Authors
  1. Hongqiang Zhu
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  2. Jianxian Qiu
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Correspondence to Jianxian Qiu.

Additional information

Communicated by: Ben Yu Guo.

The research was partially supported by NSFC grant 10931004, 11126287, 11201242, NJUPT grant NY211029 and ISTCP of China grant No. 2010DFR00700.

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Zhu, H., Qiu, J. An h-adaptive RKDG method with troubled-cell indicator for two-dimensional hyperbolic conservation laws. Adv Comput Math 39, 445–463 (2013). https://doi.org/10.1007/s10444-012-9287-7

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  • DOI: https://doi.org/10.1007/s10444-012-9287-7

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